Rachel McLeod and Barbara Newmarch
Maths4Life
Fractions
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Maths4Life
Fractions
Contents
Approaches to learning about fractions
4
Why fractions?
5
What is a fraction?
6
Introducing fractions
9
Teaching points
10
The language of fractions
11
Making connections
12
Activities
14
Classifying fractions
16
Interpreting fractions
18
Dealing with remainders
19
Evaluating statements about fractions
20
Links outside the classroom
21
Assessing understanding about fractions
21
Assessment by questioning
22
Possible questions
23
Analysing errors and misconceptions
24
Suggestions for resources
26
Some do’s and don’ts
28
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Approaches to learning about fractions
This booklet is aimed at all teachers working with learners from about entry
level 3 to level 2. It is not a text book, or a list of recipes to teach particular
aspects of fractions. Instead, it suggests some approaches that we have found
effective in enabling learners to use fractions and to relate them to other
mathematical concepts.
It is important that learners think about relationships between fractions, rather
than just trying to memorise methods for processing them. An introduction to
fractions should include a strong emphasis on developing reasoning skills,
comparing fractional amounts and exploring equivalence.
Many learners may feel that listening to the teacher and completing their own
worksheets individually is the main way of learning. However, we believe that
learners learn more if they actually enjoy the activity, have a chance to discuss
what they do, explain their work, and reach a shared understanding. There is
now widespread recognition of the value of collaborative work in developing
conceptual understanding.
Although the activities outlined in this booklet can be done individually, most of
them will work better as collaborative tasks. This approach may be unfamiliar to
many learners, particularly those whose previous maths experience was in a
more traditional classroom.
Learning is generally most effective when learners are working collaboratively.
The task could, for example, be pitched a bit higher, just outside an individual
learner’s comfort zone, so that it needs a second opinion. It may also involve
practical equipment that needs a second pair of hands. An explanation of the
benefits and ground rules is important for all learners before starting
collaborative tasks, so that each group member gets a chance to express an
opinion and challenge what others say.
In this context the teacher is not so much an instructor, as someone who asks
the right kind of questions to move discussions on, and doesn’t immediately
confirm correct answers. The teacher will want to spend time listening to the
discussion in small groups, and may join in, but should not try to replace whole
class lectures with small group ones.
As with all learning situations, the teacher will have to make some snap
decisions about how to react to situations that develop, particularly those where
a group agrees about something which is in fact incorrect. Comparison with the
work of other groups where learners have to justify their conclusions can be a
more powerful checking strategy than simple validation from the teacher.
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Collaborative learning situations tend to have a shared goal of producing an end
product, such as a poster, a presentation to the group, or a set of questions for
other learners. Discussion of the similarities and differences between posters
from different groups can be a very effective way of addressing errors.
Why fractions?
Many learners identify fractions as an area of maths that they find difficult,
despite often using concepts of sharing effectively in their daily lives. The key
question as to why so many people perceive fractions as difficult is something
we need to consider.
One reason may be the notation of fractions. Another may be the formal
vocabulary. Learners may be drowning in the language of fractions, even before
thinking about their properties.
Learners may be able to draw and label fractions correctly, but not be able to
put them in order of size, or use them to solve problems.
Fractions may also be confusing because they do not behave like ‘normal’
numbers.
Fractions sometimes represent an amount, something that can be visualised,
and sometimes an operation, e.g. 3/4 can mean a shape with 3 equal pieces
shaded out of 4; it can mean the result of dividing 3 by 4, or part of an
instruction to find, say, 3/4 of 16.
Approaches to teaching about fractions need to give learners a chance to
explain how they see them, and the teacher needs to take this into
consideration in their approach.
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What is a fraction?
A number in its own right
0.75
-3
-2
-1
0
1
2
3
|
|
|
|
|
|
|
Fractions can be shown on the number line, (e.g. 3/4 is a number between
0 and 1). Learners need to understand that the number is the result of
dividing the top number by the bottom number.
A proportion of a whole
Fractions can also be thought of as proportions/parts of a whole, (e.g. 2/3 of
the people in this group wear glasses). The teacher can talk about what this
means in terms of ‘two in every three people wear glasses’ and look at
examples with the class.
Some learners may have been introduced to
pictorial representations of fractions which
still leave them confused.
For example, the diagram on the left is fine
to explain 2/3 as a proportion. However, be
careful not to use it to explain 2/3, meaning
two things divided into three parts, as there
are clearly not two things.
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Relates to sharing objects
The third way of thinking about fractions is that they are about sharing
(e.g. sharing two pizzas between three people).
Using the example of pizzas, we show how we might share two whole
pizzas equally between three people (i.e. 2 ÷ 3):
The top picture (A) shows two whole pizzas each divided into three
slices, and the bottom picture (B) represents each person’s share
when the two pizzas have been shared between three people.
A
B
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Introducing fractions
One of the first places to start is to ask learners to think of some fractions they
have encountered in an everyday context, as a way of collecting up some
possible definitions of the meaning of ‘fraction’.
Some fraction vocabulary is used in common parlance, sometimes with rather
different meanings, or less accuracy, and this can be usefully explored. For
example, a “fraction” may sometimes mean “only a very small part” of
something, as in “a teacher earns only a fraction of a professional footballer’s
salary”. (An interesting question to ask learners is whether they think 1/4 of a
million is a big or a small number.)
Before dealing with the written symbolic form of any fractions, we can name
some of them and talk about what they mean.
We can raise some questions about fractions and encourage learners to
think of their own questions, e.g.:
When do people use fractions?
Do fractions matter if they are only small parts?
Is a half always the same size?
Can a fraction be bigger than one whole unit?
Is it possible to have three halves?
Are fractions anything to do with division?
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Teaching points
10
>
Learners should understand that one way of thinking about a fraction is to see
it as the result of dividing the top number equally into the number of pieces
shown by the bottom number.
>
A key point is that the denominator (bottom number) of a fraction shows how
many equal parts a number, or an object, or a set of objects, has been divided
into. The numerator (top number) tells us how many of those parts there are.
>
Learners need to be familiar with multiple representations of fractions, and
should always be given more than one representation. These can include: area
diagrams using a range of different shapes, number lines, words, symbols,
some decimal equivalents and percentages, fractions as a result of division.
>
Pictorial representations of a particular fraction may be of different sizes and
different shapes. For example, don’t always use shaded sections of circles, and
interesting discussions can be had from drawing half of a small square and a
quarter of a larger square and asking which is the larger fraction (and this
means you have to be careful when using areas to explain fractions!).
>
Compare unit fractions with different denominators (e.g. 1/3, 1/4, 1/5).
>
Compare fractions with the same denominator (e.g. 1/5, 2/5, 3/5).
>
Encourage strategies for deciding whether a fraction (unit or non-unit) is less
than half, equal to half or greater than half.
>
Consider the difference between a unit fraction and a whole unit (e.g. 1–1/4 or
1–1/5).
>
Show that each fraction can be written in an infinite number of equivalent
forms.
>
Show that fractions can be equal to, or bigger than one whole.
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Fractions
The language of fractions
Much of the language involved in working with fractions needs to be taught
explicitly in context.
Learners need to be encouraged to use the vocabulary which describes the
concepts they are exploring. Initially, this should include:
‘whole numbers’
naming of fractions: e.g. ‘half’, ‘quarter’, ‘third’, ‘tenth’
‘divide’, ‘share’
‘equal parts’
‘out of’
‘halves and doubles’
comparison vocabulary: ‘more than’, ‘less than’, ‘equal to’, ‘the same as’
‘left over’, ‘remainder’
Some formal fraction language may, for some learners, be linked with
mechanistic notions of following rote-learned ‘recipes’ for fractions and may
serve to confuse or distract them from thinking about the meaning of what they
are doing. We suggest that it is usually a good idea to delay use of these terms
until a later stage, once the basic concept of a fraction is reasonably secure and
the need for identifying procedures arises:
‘cancel’, ‘reduce’,‘simplify’
‘lowest terms’
‘denominator’
‘numerator’
‘lowest common denominator’
‘highest common factor’
‘top heavy’
‘equivalent’
‘proper’, ‘improper’
‘mixed numbers’
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Making connections
All too often learners think of ‘fractions’ as being a discrete (and often difficult)
topic that has no real connection with any other area of maths. However,
meaningful connections make learning more powerful. We can use the
knowledge and experience that all adult learners already have of fractions,
particularly halves and quarters, and also the fractions that are part of everyday
language.
Work on fractions needs to be integrated into other maths topics; number,
shape, data handling, and particularly every sort of measure of weight, length,
capacity, time, and simple probability. Learners will encounter fractions
throughout their work at all entry levels of the numeracy curriculum, e.g.
solving money problems, sharing a bill, comparing prices, calculating journey
times, cooking, interpreting data in pictograms and bar charts, using a metre
rule, measuring a room, comparing each other’s heights, and checking the
weight of ingredients.
Learners should be encouraged to see that developing their skills in
multiplication and division is an integral part of understanding and using
fractions. Learning about fractions involves learning about relationships
between numbers, exploring number patterns and sequences, developing
estimating skills, using measurement and problem solving.
Instead of feeling that ‘decimals’ or ‘percentages’ are completely different
topics, learners need plenty of experience, even at an early stage, of seeing that
these are simply other ways of representing fractions.
Learning about decimal place value, and the relationship between metric units,
or between pounds and pence, can be one of the starting points for talking
about fractions. It is important for learners to see that decimal notation is
another representation of tenths and hundredths, and to develop familiarity
with these fractions.
Learners may need to know how to input a fraction into a simple calculator and
read the decimal fraction. They should have plenty of experience doing this to
explore the connections, rather than trying to learn these by rote.
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Any work on fractions, such as matching equivalents, should include some
basic decimal and percentage representations as well (e.g. 0.5, 50%, 1/2, see
http://www.bbc.co.uk/skillswise/numbers/fractiondecimal
percentage/comparing/comparingall3/)
Although the Adult Numeracy Core Curriculum identifies specific skills and
knowledge about fractions as elements at each level, this should not be seen
as a set of hard and fast rules. If learners are encouraged to understand and
explore fraction concepts, their work on fractions may well spread across more
than one ‘level’.
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Activities
SHARING CAKES
This activity includes four sets of cards, all to be cut up and matched. The
learners themselves can do the cutting up, as the sheets are arranged so that
the answers are not all in the same sequence.
One set has diagrams of the cakes. On these cards, learners would need to
show, by shading parts of whole cakes, or drawing lines between the cakes,
how the cakes would be shared so that each of these cards matches one
from each of the other sets.
To download these activities go to www.maths4life.org
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Fractions
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Classifying fractions
Classifying different representations of fractions, or statements about them,
can be a very effective method of encouraging learners to reflect on and
discuss their properties. Learners may group together different representations
of the same fraction: in a picture, in words, on a number line, as a decimal.
They may classify them according to their size, or classify statements about
fractions as true or false. (See example activities at www.maths4life.org)
This is an approach that lends itself to differentiation within the group, with
learners using different classifications depending on previous experience of
fractions.
One possible activity is for all learners in a group to be given fraction cards and,
working in pairs, to sort them into different categories (opposite). This might
prompt a discussion as to whether all fractions with denominators 2 and 3
would be included on this grid (no, those equal to 1 are excluded). Alternatively,
they could choose their own fractions, and write their own cards, to go in each
category.
As a follow-up learners can choose their own categories for classification. In
addition to mathematical categories, it is interesting to encourage learners to
include categories like ‘easy’ and ‘hard’ and explicitly discuss why some
fractions are harder than others. More challenging problems can be devised for
others by putting the fractions in spaces on the classification grid so that other
learners must guess the headings used.
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Interpreting fractions
Given their different representations, and the way they sometimes refer to a
number and sometimes an operation, it is important to be able to discuss
fractions in the many ways they appear. A multiple representation activity,
including different numerical and visual representations, is one way of doing
this. (See example activities at www.maths4life.org)
Sharing food is a good way to introduce various concepts aboput
fractions. For example, using a chocolate bar and dividing it into pieces.
This can be highly motivating if learners can eat it afterwards!
A clock face shows clearly what halves and quarters look like, and can be
extended to other fractions with discussion about why some are easier to
show than others. We can find a third of an hour, but what about a fifth?
A paper tape measure (like those from IKEA) is a valuable illustration of
different fractions. For example, learners can write on 1/2m, 0.50m and
50cm for their own portable equivalence chart.
I have ten bars of chocolate, and I share them equally
between four people. How much will they each get?
We recommend that teachers explicitly use the language of fractions in other
parts of the curriculum for reinforcement. For example, when looking at
shapes, talk about ‘half a square’ and ‘third of a circle’. You could also talk
about when fraction talk is not appropriate, for example, “it is half as hot as
yesterday” does not make sense.
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Dealing with remainders
Learners can often be confused about what to do with remainders after
division. They may not be sure when to ignore remainders, to round them up, or
to show what is left over as a fraction or a decimal. Different decisions need to
be made about how to interpret the remainder, and what makes sense,
depending on the context.
Learners need to explore problems in a range of situations, all involving the
same division calculation, e.g. a problem which involves dividing 10 by 4,
depending on the context, may have as an appropriate solution 3, 2, 2.50, 21/2 or
as “2 remainder 2”.
Ten people need to travel by taxi from the airport to the city centre.
A taxi can only take four passengers. How many taxis will be needed?
You want to buy CDs costing £4 each.
You have £10. How many of these CDs can you buy?
You are sharing £10 between four people.
How much will they each get?
I have ten bars of chocolate, and I share them equally between four
people. How much will they each get if I don’t split the bar? And how
much will they each get if I do split the bar?
Learners can practise writing their own sets of contexts for division problems
that will involve different decisions about what to do with the remainder.
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Evaluating statements about fractions
Learners are given some generalisations about fractions, perhaps printed out
on separate cards, and are asked to choose whether they consider these to be
‘always’, ‘sometimes’ or ‘never’ true, and to justify their choices, with examples
and convincing explanation. The statements may deliberately include common
misconceptions. This activity needs to be an in-depth discussion, initially in
pairs or small groups, and then with the whole group.
Each learner in turn should choose one statement. Others should be
encouraged to argue and challenge, and to refine their reasoning.
Once they have agreed on a verdict, they can make a poster for display in the
classroom. They could also think of some statements for other learners to
consider in the same way.
Here is a sample: (for an example of these see www.maths4life.org)
A fraction is a small piece of a whole
When you multiply one number by another the answer
must always be bigger
You can’t have a fraction that is bigger than one
Five is less than six so one fifth must be smaller than one sixth
Any fraction can be written in lots of different ways
Fractions don’t behave like other numbers
Decimals and fractions are completely different types of numbers
Every fraction can be written as a decimal
Every decimal can be written as a fraction
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Links outside the classroom
Experience has shown us that many learners do not use their understanding of
fractions outside the classroom, and are unwilling or unable to transfer it to
‘real life’ problems. For example, a learner could work out 1/3 of 30 million, but
had no idea how to work out 2/3 of 30 million (from a news story about women
with AIDS in Africa).
As suggested in the curriculum, take a headline or advert and make a poster to
explain what it means. For example, a July 2005 headline says that one in three
11-year-olds have smoked. What fraction is this? How many people does that
represent in an average school? How many in the UK? Should we worry about
this? To link with the problem above, encourage learners to think about the
11-year-olds that have not smoked.
A healthy diet should include no more than 60g of fat in a day. Collect food
labels and other nutritional information and find out what fraction of the daily
fat allowance is in a bag of crisps. Using a grid of 60 squares, and by rounding,
learners can work out the fraction of their daily limit in different foods, and
express this using equivalent fractions. A bag of crisps, for example, has about
1/6 of the guideline daily amount.
The proportions of the human body provide links with art, and with
dressmaking/tailoring. For example, artists assume the eyes are half-way down
the face, the nose half-way between the eyes and the chin. A tape measure and
some sketching can check the truth of these rules.
Assessing understanding of fractions
Assessment can take many forms. In many numeracy classes assessment of
learning is summative - checking that a learner can successfully complete a
worksheet on a topic independently, and pass a test.
The majority of adult learners have ‘done’ maths before, and this probably
included some work on fractions, yet they sometimes still identify fractions as
an area of difficulty. This suggests that we need a much broader approach to
assessment.
Our formative assessment tools need to find out what learners have covered
before, rather than assuming they are meeting fractions for the first time. They
need to identify what has been mislearned or is difficult to conceptualise. Class
questions, which everyone has a chance to think about and answer, can provide
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a valuable starting point for discussion.
One of our most valuable assessment tools is silence. Standing back and
listening to learners explaining their thinking can be a more powerful
assessment tool than any number of written diagnostic tests.
In addition, we can make creative use of summative assessment: for example,
learners can write their own exam-style questions. By inserting their own
figures, or rewriting questions, they may become confident at writing their own
new questions from scratch.
Assessment by questioning
Questioning can be used by teachers to find out very specifically whether a
particular learner knows the answer to a particular closed question, e.g.
drawing a shape on the board and asking what fraction is shaded. However, it
can be used much more broadly for formative assessment and to encourage
deep mathematical thinking.
Before introducing a topic, a few well-chosen questions can help to identify
what learners already know, or what they learned from previous sessions (e.g.
asking them all to show something that means ‘half’). We have had valuable
conversations in class, addressing a number of misconceptions, using learners’
correct and incorrect answers as starting points.
Having asked questions, teachers need to consider what to do with learner
responses. It may be appropriate to try to work out what has led to an incorrect
response. Some flexibility is needed in deciding how far to follow a line of
enquiry which was not planned for the lesson.
Questioning to learners about why they are doing something is a good way of
uncovering their thinking processes. Devil’s advocate questions (e.g ‘isn’t
remainder 5 the same as 0.5?), or ‘What if…?’ questions can help to see
whether learners have developed a general understanding of a concept.
Learners may already feel comfortable asking questions, but it is also possible
to set up situations where they need to question each other. In all situations,
ensure everyone has time to think before they respond.
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Some possible questions about fractions
1. Using mini whiteboards
“Show me a fraction (encourage naming in words, using numbers and
diagrams). Show me a harder fraction.”
“Show me a question where the answer is 6. Now use 1/2 in the question. Now
use 1/4. Now make a really hard question. Show me a question where the
answer is 2 1/2”
“Here is half a shape (drawn on board), what could the whole shape look like?
Similarly for 1/4, or 1/3 as appropriate.” (When collecting answers on the board,
ask learners to describe shapes as a way of reinforcing idea of equal pieces)
“Show me a fraction bigger than 1/4. Show me a fraction between 1/2 and 1,
between 3/4 and 1, bigger than 1…”
(Encourage learners to draw diagrams and represent on number lines)
“Which is the odd one out: 1/2, 1/4, 2/4? or 1/4, 2/5, 0.4? Can you make each of
them the odd one out?”
2. To understand reasoning
“Why are 1/3 and 2/6 the same?”
“Why did you change 3/4 to 9/12? Suppose you were comparing 3/4 and 5/8:
What would you do then?”
“How did you work out that 2/3 of 60 million was the same as 40 million? How
would you explain your method to someone who hadn’t done this kind of thing
before?”
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Analysing errors and misconceptions
Some misconceptions about fractions may be immediately apparent; however,
it is also important to find strategies for uncovering learners’ thinking
processes and seeing errors that might lie below the surface. Sometimes
learners appear to give a correct response, but their reasoning misfires.
It is important to encourage learners to voice their ideas, even if they are based
on misconceptions. It is only when these are really out in the open that they can
be effectively addressed.
Some learners may identify this diagram as
representing 1/3 because they see it as one
shaded over three unshaded.
Some learners see some fractions, e.g. 1/3 and 1/4, as interchangeable. This
may be because the words ‘quarter’ and ‘third’ do not suggest the numbers 4
and 3. It may be worth checking to see if your learners have these
misunderstandings.
Often visual representations of fractions may have been used only in a limited
way. Some commonly used fractions tend to be shown in certain shapes. So
learners may have seen 1/4 shown in a square, but 2/3 only shown in a circle.
Diagrams need to be used carefully so as not to confuse learners and to enable
them to make meaningful comparisons. Representations of fractions on
number lines, reinforcing both their size and decimal equivalents are just as
important.
Even when the same shape has been used to help comparison, learners may
find it difficult to reconcile what they see with the way they read the
combination of two numbers in a fraction. Some explain that although a
diagram clearly shows that 1/8 is bigger than 1/16, the 16 in their minds
somehow takes over and tries to tell them 1/16 is a bigger number.
Looking at two positive whole numbers it is clear which is bigger. With 1/16 and
this may also be clear. However, moving away from unit fractions, even this
1/8
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‘rule’ does not apply. For instance, 3/8 is bigger than 5/16, but 3/16 is bigger than
1/8. Learners trying to use the size of the top and bottom numbers as the key to
comparison could feel they were on very shaky ground by now.
Here are some more examples of common mistakes:
“ 2/3 – that’s two and three”
Seeing the numbers in a fraction as two unrelated whole numbers separated
by a line
“ 1/3 + 1/4 = 2/7”
Treating fractions in the same way as whole numbers
“ 1/4 = 1.4”
Being influenced by appearances
“ 4/5 > 1/3 because 5 > 3”
Thinking that it is only the denominator that determines the size of the fraction
“ 1/2 + 1/2 = 2/4”
Not being able to judge that an answer does not make sense
“Anything less than a half is a quarter” or “ 1/3,
that’s the same as 1/4 isn’t it?”
Not understanding the concept of fractional parts
“ 7/2=2.1 because three goes into seven twice with one left over”
Not understanding what to do with a remainder and what 0.1 actually
represents
“ 1/3 of 30 is … 3 ?”
Not understanding that one third is the same as dividing by three
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“ 3/4 of 12 pens is … four because that’s quarters …?”
Not having sufficient experience of fractions as parts of sets of objects
“There are three quarters in a whole because two is half”
Not understanding the relationship between the fractional part and the unit
“ 2/10 – that’s two tens”
Confusion about “tens” and “tenths”, “hundreds” and “hundredths” because
they sound the same
Unequal partitioning of area diagrams to
represent fractions other than half or
quarter, not understanding that the
divisions need to be equal.
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Suggestions for resources
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Readers are advised to read the background to these approaches. Full details
of the work undertaken by Malcolm Swan of the University of Nottingham and
Susan Wall of Wilberforce College, Hull, together with the DfES Standards
Unit, can be found at
http://www.maths4life.org/content.asp?CategoryID=1068
Mini-whiteboards and whiteboard pens
These enable learners to easily jot down responses, and work out ideas,
freeing them from worry about crossing out mistakes.
Sets of fraction cards with fractions in numbers, area diagrams, number
lines, percentages and decimals
These can be cut up and laminated if appropriate, or they can simply be printed
out for each session and cut up by the learners themselves.
Number lines, both numbered and blank
A useful way of modelling fractions. Blank number lines which learners can
annotate themselves are useful.
Counting sticks, metre sticks, rulers, tape measures
Fraction wall (see BBC Skillswise www.bbc.co.uk/skillswise/)
Fraction dice (use ordinary dice with fraction stickers)
Calculators
2D and 3D fraction sets
OHP resources including transparent coloured fraction blocks, number lines,
clock faces, calculators
Fraction dominoes
These can be custom-made, using a basic template, for matching fractions in
various representations.
Sets of cubes, both separate and interlocking
A range of measuring equipment, e.g. scales, balances, weights, measuring
jugs and beakers of different capacities, calibrated in different ways
Digital clocks with moveable hands, blank clock faces
1 cm and 2 cm squared paper
Tangrams
Coloured counters, Post-It notes, index cards, tracing paper, scissors, card,
glue sticks, string.
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Some do’s and don’ts
Do
Do
Find out and start from what learners know
Be sensitive to the fact that many learners may have previously found
work on fractions difficult and frustrating
Talk about how fractions are used in everyday life
Encourage learners to estimate with fractions
Make sure any activities are enjoyable, stimulating and include
group work
Show fractions in a variety of representations
Encourage learners to talk about fractions
Support learners in checking their own work
Give lots of thinking time when you ask questions
Delay using formal fraction vocabulary until learners are ready
Use tenths and hundredths and encourage learners to see decimals as
another representation of fractions
Make connections with other maths topics
Don’t
Use lots of visual aids
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Don’t
Introduce formal fraction symbols too early
Teach learners to memorise processes and rules
Teach just halves and quarters, even from the start
Allow learners to compartmentalise fractions or to see them as
‘separate’ from decimals and percentages
Give endless drills and ‘practice’
Tell learners all the answers
Maths4Life
Fractions
Notes
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Maths4Life
Fractions
Notes
30
About the authors
Rachel McLeod trained as secondary maths teacher.
She started working at Tower Hamlets College in 1991,
and had a variety of different roles. After two years in
Japan, teaching English to business people and
mathematics to young people at an International
School, she returned to Tower Hamlets as Adult
Numeracy Coordinator in 2004. Rachel has recently
been working on a level 4 numeracy subject specialist
course and is involved in Standards Unit pilot and the
Maths4Life pathfinder project.
Barbara Newmarch teaches numeracy/mathematics in
two London colleges, and also runs numeracy teacher
training courses. She has been a teacher-researcher
on a NRDC project, ‘The teaching and learning of
common measures in adult numeracy’, and a
Maths4Life project on ‘Formative assessment in adult
numeracy’. She has written a guide ‘Developing
Numeracy’ in the NIACE ‘Lifelines in Adult Learning’
series.
This booklet is produced by Maths4Life to
provide teachers of adult numeracy with
some ideas about how to teach fractions. The
aim is to examine why learners may find it
difficult and to describe ways which the
reflective teacher can overcome these
difficulties. Accompanying sample resources
can be found at www.maths4life.org